Thus the consistency conditions encoded in the process matrix formalism offer a partial explanation for the prominence of causal order in the physical world, as well as the apparent absence of causal order for processes like measurements on entangled particles. However it is only a partial explanation, because we can also use the process matrix formalism to write down non-causal processes which obey the consistency conditions, so something more than just consistency conditions is needed to explain why it seems that all physical processes are causal, or at least why the regimes we have so far probed contain only causal processes. For example, ref [1]} proposes that all physical processes should be `purifiable,' i.e. they should be expressible as part of a pure process in a larger space, where a pure process is one that induces a unitary transformation from the past to the future whenever unitary transformations are also applied in the local laboratories. It is shown that this rules out a large class of non-causal processes, although not all of them. Several other arguments are presented in ref [2]}. First, if we allow non-causal processes, then the dynamics of the allowed processes cannot be defined in a local way, since certain sorts of dynamics are possible outside closed timelike curves and exotic causal structures but are not always possible inside such structures - e.g. we saw in section  that in the classical process function approach the identity operation around a closed timelike curve is not possible, but evidently the identity operation is possible outside closed curves. One might argue that this novel kind of nonlocal dependence on the global structure of spacetime is not permitted by the laws of our actual world, and thus non-causal processes are not physically possible. Second, the notion that non-causal processes are possible relies crucially on the idea that there is a fundamental distinction between local operations in laboratories, which can be freely chosen, and dynamics between the laboratories, which are fundamentally uncontrollable - for example, the framework must have the consequence that if we try to implement the identity operation around a closed curve we will always fail. And yet in a sense one can think of dynamics as being just a sequence of chained local operations, so one might feel that the distinction being made here is too strong: if we have free choice over local operations, we should also be able to freely construct dynamics on a CTC by means of chains of local operations. This line of reasoning might be taken to suggest that these sorts of non-causal processes are not in fact physically possible - or at least they should not be possible in the kinds of regimes where we can in principle have very good control over the dynamics we implement, which would explain the fact that we have not observed any of them in the regimes we have thus far probed. In any case, if some such argument is accepted, we can then argue that the necessity for all signalling processes to exhibit causal order follows directly from the need to avoid contradictions, and thus the causally ordered nature of the physical world can be regarded as a simple consequence of basic consistency conditions.
